Probing the Inner Region of Cyg X 1 in the Low/Hard State through its X-ray BroadBandSpectrum

Transcription

1 Probing the Inner Region of Cyg X 1 in the Low/Hard State through its X-ray BroadBandSpectrum T. Di Salvo 1,C.Done 2,P.T.Życki3, L. Burderi 4,N.R.Robba 1 ABSTRACT We present the broad band X-ray spectrum of Cyg X 1 in the low/hard state as observed by the instruments on board of BeppoSAX. The spectrum spans from 0.1 to 200 kev, allowing the total accretion luminosity to be observed, rather than extrapolated, corresponding to 2 per cent of the Eddington limit for a 10 M black hole. The broad bandpass allows us to determine the continuum shape with great accuracy. Simple models of Compton up-scattering of seed photons from the accretion disk do not adequately match the spectrum. At low energies an additional continuum component is required, giving a complex soft excess which extends up to 4 kev, in line with previous results from ASCA. Moreover we clearly detect a reflected component from the accretion disk which is smeared, probably because of relativistic and Doppler effects. The reflecting material is not strongly ionized and does not subtend a large solid angle as seen from the corona (Ω/2π ). The inner radius of the disk, that depends on the inclination of the system, is most probably between 10 and 70 gravitational radii (R g ). An unsmeared reprocessed component, probably originating from the companion star or the outer disk, could also be present. In this case, the inner radius of the disk, as inferred from the smeared reflection, is smaller, between 6 and 20 R g. Subject headings: accretion discs stars: individual: Cygnus X 1 stars: black holes X-ray: stars X-ray: general 1. Introduction Cyg X 1 is the brightest of the persistent galactic black hole candidates. It is a binary system consisting of a black hole accreting matter from a supergiant type O star. It shows (at least) two different spectral states, namely a high/soft state where the luminosity is dominated by strong blackbody emission at low energies (kt =0.5 1 kev), and a steep power law (photon index 1 Dipartimento di Scienze Fisiche ed Astronomiche, Università di Palermo, via Archirafi n.36, Palermo, Italy 2 Department of Physics, University of Durham, South Road, Durham, UK 3 Nicolaus Copernicus Astronomical Center, Bartycka 18, Warsaw, Poland 4 Osservatorio Astronomico di Roma, Via Frascati 33, Monteporzio Catone (Roma), Italy

2 2 Γ > 2 3), extending out to at least 800 kev, is also present, and a low/hard state, which has much less soft emission (kt = kev), and has the luminosity dominated by a hard power law (Γ ) which cuts off at 200 kev. In addition to the continuum emission other spectral features are present in the spectrum, most noticeably an iron K α line and edge at 6.4 and 7.1 kev respectively. These features are seen in both spectral states, and can be fit with models of X-ray reflection of the power law from an accretion disk (Done et al. 1992; Gierliński et al. 1997, 1999). Detailed spectroscopy of the reflected spectrum can be used to probe the accretion flow, since its amplitude and shape are determined by the ionization state, geometry and velocity field of the reprocessing plasma. Ionization of the reprocessor decreases the photoabsorption opacity, thus increasing the reflection albedo at low energies, as well as the energy and intensity of the iron K α fluorescence/recombination line, and energy and depth of the iron K edge (Lightman & White 1988; Ross & Fabian 1993; Życki et al. 1994). The normalization of the reflected spectrum for a given ionization then depends on the inclination angle of the accretion disk with respect to the observer and on the solid angle subtended by the disk to the hard X-ray source (George & Fabian 1991; Matt, Perola & Piro 1991). The combination of Doppler effects from the high orbital velocities and strong gravity in the vicinity of a black hole smears the reflected spectrum, so that the line (and the reflected continuum) has a characteristically skewed, broad profile, whose detailed shape depends on the inclination and on how deep the accretion disk extends into the black hole potential (Fabian et al. 1989). The best known example of the effects mentioned above is the Fe K α line profile in the spectrum of the Seyfert 1 galaxy MCG (Tanaka et al. 1995). The amount of reflected spectrum is that expected for a disk which covers half the sky as seen from the X-ray source (Lee et al. 1999). The fit of the iron line profile implies that the inner edge of this reprocessor lies at (or even within) the marginally stable orbit in Schwarzschild metric R ms =6R g (R g GM/c 2,whereGis the gravitational constant, M the mass of the black hole, and c the speed of light) (Tanaka et al. 1995; Iwasawa et al. 1996). These effects should also be present in Galactic Black Hole Candidates (GBHC), and should be more easily observable because of the much higher signal-to-noise ratio. Yet in the low/hard state of Cyg X 1 the amount of observable reflection is smaller than expected for a complete disk (e.g Gierliński et al. 1997) and the amount of relativistic smearing is less than that seen in MCG , implying that the disk terminates at 10 20R g rather than extending down to the last stable orbit (Done & Życki 1999). Other low/hard state data from GBHCs show the same lack of extreme relativistic smearing as Cyg X 1 (Życki, Done & Smith 1997; 1998; 1999; Gilfanov, Churazov, & Revnivtsev 1999), as do some AGN (IC 4329a: Done, Madejski, & Życki 2000; NGC 5548: Chiang et al. 2000). In this respect MCG has an exceptionally steep X-ray spectrum, so it is more comparable to the high/soft state of GBHCs rather than to the low/hard state discussed here (Zdziarski, Lubiński & Smith 1999). If the standard optically thick, geometrically thin disk does truncate before the last stable orbit this could indicate that inside this transition radius (R tr >R ms ) the accretion changes to a hot, optically thin, geometrically thick flow, most plausibly an advection dominated accretion flow

3 3 (ADAF: see e.g. Narayan 1997 for a review). Such a geometrical configuration is compatible with the overall broad band spectral shape of Cyg X 1, which has a rather hard (photon-starved) spectrum, as well as with the observed low amplitude of reflection and relativistic smearing (Poutanen, Krolik & Ryde 1997; Gierliński et al. 1997; Dove et al. 1997; review in Poutanen 1998). The alternative models which keep an untruncated disk are reviewed in Done & Życki (1999). These models require that the hard X-rays are produced in active regions above the disk, probably powered by magnetic reconnection (Galeev, Rosner & Vaiana 1979; Haardt, Maraschi & Ghisellini 1994). There are two plausible ways for the untruncated-disk models to match the spectral constraints. First, the models in which the X-ray emission regions expand with relativistic velocities away from the disk (Beloborodov 1999a,b): this suppresses both the seed photons for Compton scattering (so giving the observed hard spectrum) and the amount of reflection (by beaming the observed X-ray spectrum away from the disk). The second possibility is that the X-ray illumination photo-ionizes the disk reducing the photo-electric opacity. In this case there are no spectral features in the reflected spectrum, since it is formed purely from Thomson scattering. The large fraction of flux reflected means that this also decreases the thermalized fraction of the primary X-rays, so there are few soft photons (Ross, Fabian & Young 1999; Nayakshin, Kazanas & Kallman 2000). Distinguishing between these various models should surely be possible from detailed studies of the reflected spectrum and energetics of the continuum spectrum. However, the derived parameters for the amount of reflection and smearing depend crucially on how the continuum is modelled and there is increasing evidence that simple thermal disk blackbody and comptonized power laws are not sufficient to describe the spectrum, especially at low energies where ASCA data show an additional soft component below 3 4 kev in Cyg X 1 (Ebisawa et al. 1996). The continuum can be better characterized with a broad bandpass, and we report here on the BeppoSAX kev observation of Cyg X 1 in the low/hard state. We show that there is indeed a complex soft component, and that the reflected continuum can be clearly disentangled from this complex spectrum. 2. Observations The BeppoSAX Narrow Field Instruments (NFIs) observed Cyg X 1 on 1998 May 3 and 4, for an effective exposure time of 25 ks. The NFIs are four co-aligned instruments which cover more than three decades of energy, from 0.1 kev up to 200 kev, with good spectral resolution in the whole range. LECS (operating in the range kev, Parmar et al. 1997) and MECS (1 11 kev, Boella et al. 1997) have imaging capabilities with a Field of View (FOV) of 20 and 30 radius respectively. In these FOVs we selected the data for the scientific analysis in a circular region of 8 and 4 radius for LECS and MECS, respectively, around the centroid of the source. The background subtraction was obtained using blank sky observations in which we extracted the background data in a region of the FOV similar to that used for the source. HPGSPC (7 60 kev, Manzo et al. 1997) and PDS ( kev, Frontera et al. 1997) do not have imaging capabilities, because the FOVs, of 1 FWHM, are delimited by collimators. The background subtraction for these instruments was

4 4 obtained using the off-source data accumulated during the rocking of the collimators. The energy ranges used for each NFI are: kev for the LECS, kev for the MECS, 8 30 kev for the HPGSPC and kev for the PDS. We added a (conservative) systematic error of 5% to the PDS data, to take into account calibration residuals 5. Different normalizations of the four NFIs are considered by including in the model normalizing factors, fixed to 1 for the MECS and kept free for the other instruments. The same method has been used to fit Crab spectra (Massaro et al. 2000), obtaining photon indices which are within α 0.03 of those expected from models of the synchrotron emission (Aharonian & Atoyan 1995). During the BeppoSAX observation Cyg X 1 was in its usual low/hard state with a total ( kev) unabsorbed luminosity of ergs/s, adopting a distance of 2 kpc (e.g. Massey, Johnson, & Degioia-Eastwood 1995, Malysheva 1997). Figure 1 shows the MECS light curves in three energy bands, 1 4 kev (first panel from above), 4 7 kev (second panel) and 7 11 kev (third panel), and the corresponding hardness ratios. Although the MECS light curves show an increase of the intensity up to 30 % during the observation, the hardness ratios appear to be constant, except for a little hardening at the end of the observing period (between and s). This hardening is probably due to an absorption dip, because it is visible in the soft range and disappears in the hard range. Cyg X 1 is known to show intensity dips, which preferentially occur near the superior conjunction, at the orbital phase φ = 0, although dips were also observed at φ =0.88 and φ =0.42 (Ebisawa et al. 1996). The BeppoSAX observation spans the orbital phase interval φ = (using the ephemeris reported in Gies & Bolton 1982), and the observed dip occurs at phase φ = We excluded this dip from the following spectral analysis. 3. The Spectral Model The direct comptonized component from the corona is modeled by the thcomp model (Zdziarski, Johnson & Magdziarz 1996), obtained by solving the Kompaneets equation. To describe the reflection component we use the angle dependent reflection model of Magdziarz & Zdziarski (1995) with a self-consistent iron emission line calculated for the given ionization state, temperature, spectral shape and metal abundances, as described in detail in Życki et al. (1999). The total reprocessed component can be smeared to take into account the relativistic and kinematic effects of disc emission (Fabian et al. 1989). This is done by convolving a spectrum with the XSPEC diskline model, parametrized by the inner and outer radius of the disk, R in and R out,and the irradiation emissivity exponent, α, F irr r α.wefixr out =10 4 R g, α = 3 and fit for R in,in order to obtain an estimate of the inner radius of the accretion disc. The reflected spectrum also depends on the inclination of the system with respect to the line of sight, but this parameter is more difficult to obtain for Cyg X 1 than for most other GBHCs since 5 see the web page at

5 5 the companion O star loses matter via a strong wind, so it does not need to completely fill its Roche lobe in order to provide the accreting material. The lack of X-ray eclipses requires i<64,and almost all angles between this and 25 have been derived from spectrophotometric studies (see e.g. Ninkov, Walker & Yang 1987). Recent Doppler tomography studies of the Hα and HeII lines set an upper limit to the inclination of 55 from the fact that the emission lines from the stream were not eclipsed (Sowers et al. 1998). However, this computation used the companion star radii of Gies and Bolton (1986), which have been shown to be overestimated (Herrero et al. 1995). Thus we repeat the fits for a wider range of inclination angles to quantify how sensitive our results are to this parameter. Other unknown parameters affecting the reflected spectrum are the elemental abundances. We fix these at solar (Morrison & McCammon 1983), except for iron which is allowed to vary. 4. Spectral Analysis Spectral analysis was performed in XSPEC v. 10 (Arnaud 1996), with all the non-standard spectral models implemented as local models. In Figure 2 we show the result of a fit of the kev spectrum of Cyg X 1 with a simple photoelectric absorbed power law (the χ 2 /d.o.f. was 2008/274). In the residuals (in unit of σ, lower panel) all the features expected in Cyg X 1 spectrum are clearly visible, namely the soft excess, the iron line and edge, and the spectral hardening due to the reflection at 20 kev. We tried to fit the kev energy spectrum of Cyg X 1 with a simple model consisting of a direct comptonized spectrum described by the thcomp model, the corresponding reflected component, a blackbody to describe the soft emission, and photoelectric absorption by cold matter. The temperature of the soft seed photons for the Comptonization was fixed to the temperature of the blackbody. We also fixed the iron abundance to the solar value and cos i =0.6, where i is the inclination angle (see Done & Życki, 1999). This model gives a poor fit with a χ2 /d.o.f. = 934/681. In the fit residuals there are indications for a more complex shape of the soft component The soft component Ebisawa et al. (1996) studying ASCA data of Cyg X 1 in the hard state, found that the shape of the soft component is not well described by a simple blackbody spectrum. They obtained a good fit using a blackbody plus a steep power-law tail. This is a rather unphysical description as the bolometric luminosity is infinite, so instead we use an additional comptonized spectrum described by the comptt model (Titarchuk 1994). This improved the fit significantly, giving χ 2 /d.o.f. = 713/679, using a reflection model without relativistic effects (model 1 in Table 1), and χ 2 /d.o.f. = 689/678 considering the relativistic smearing of the reflection component (model 2 in Table 1). In both cases the seed photons for the additional comptonized component were tied to the blackbody temperature,

6 6 and the electron temperature is 3 kev. The optical depths reported in Table 1 are calculated for spherical geometry of the comptonizing region; for a slab geometry it is roughly half the previous value. The large uncertainties on the temperature and optical depth of this component are due to the fact that these parameters are correlated to each other and are not well constrained individually. We have also found that using a multi-color disk blackbody (diskbb in XSPEC, Mitsuda et al. 1984) instead of a blackbody to fit the soft emission does not improve the fit. The soft excess is significantly detected using just the LECS and MECS data, showing that it is not an artifact of slight discrepancies in cross-calibration between the instruments, amplified by the broad bandpass covered by BeppoSAX. A blackbody spectrum, together with a comptonized continuum and relativistically smeared reflection, gives χ 2 /d.o.f. = 566/437, while adding the comptt component this reduces to χ 2 /d.o.f. = 510/434. Using an additional blackbody, with a temperature of 0.4 kev, instead of comptt, as a description of the soft excess, we obtain χ 2 /d.o.f. = 785/680, without relativistic smearing of the reflection component, and χ 2 /d.o.f. = 749/679 considering the relativistic effects. The first description, using the comptt model for the soft excess, thus appears to be somewhat better, but we will consider both these possibilities in the Discussion. Different descriptions of the soft excess give somewhat different estimates of the bolometric (unabsorbed) luminosity. In the first model (blackbody plus comptt) the unabsorbed flux in the two soft components is F soft erg cm 2 s 1, while it is only erg cm 2 s 1 in the second model (two blackbodies). Using multi-color disk blackbody and comptt we obtain rather larger F soft erg cm 2 s 1. The hard flux is the same in all models, F hard erg cm 2 s The hard component Adopting now the blackbody plus comptt as description of the soft component we proceed to investigate the hard component in the spectrum The Comptonized continuum The comptonized continuum is well described by the thcomp model. The spectral slope derived from the data is Γ 1.67 and the electron temperature is kt e 140 kev (these values were obtained for parameters of the reprocessing component cos i = 0.78 and Fe abundance of 2 Solar, see Section 4.2.2, but they are nearly independent of particular values chosen). The thcomp model is known to give rather inaccurate temperature estimations for temperatures above 100 kev (A. Zdziarski, private communication). We have therefore performed Monte Carlo simulations in order to derive the physical value of kt e. Using the Monte Carlo code described in Appendix A of

7 7 Życki et al. (1999) we obtain kt e 90 kev. The value of temperature is nearly independent of the plasma cloud geometry assumed, contrary to the value of optical depth, which we will discuss later in Section The reprocessed component The total model with the reprocessed component without relativistic smearing yields χ 2 /d.o.f. = 713/679 (model 1 in Table 1). Allowing now for relativistic smearing of the reflection component we obtain a better fit with χ 2 /d.o.f. = 689/678 (model 2 in Table 1). An F-test demonstrates that the probability of chance improvement of the fit is In this case, the inner radius of the disk, as inferred from the reflection component, is 130 R g, and the reflection amplitude is Ω/2π 0.3, where Ω is the solid angle subtended by the reflector as viewed from the corona. To constrain the iron abundance and the inclination angle i of the system we fitted the data using different values of these two parameters. In particular we considered cos i = 0.87, 0.71, 0.60, 0.50 and [Fe] = 3, 2, 1.5, 1 Solar abundance (the grid of models for the Fe K α line does not allow us to test Fe abundances > 3 Solar). The resulting values of χ 2 and R in are reported in Table 2. We note that the inferred inner radius of the disk is strongly dependent on the inclination as well as iron abundance. Generally we obtain larger radii in correspondence of high inclinations, because in this case the Doppler shifts, due to the orbital velocity of the matter, are stronger, giving substantial broadening. Nevertheless, we always obtain radii smaller than 150 R g,withthe most probable values lower than 70 R g. The best overall fit is obtained for cos i =0.87 and [Fe] = 2, corresponding to an inner radius of 10 R g. However we obtain an equivalently good fit for cos i =0.78 and [Fe] = 1.5, corresponding to an inner radius of 70 R g. To compare the results we plotted in Figure 3 the contributions to the χ 2 as a function of the energy in the iron line range for various models. Model 1 of Table 1 with a not relativistically smeared reflection is shown in the upper panel, the model corresponding to cos i =0.78 and [Fe] = 1.5 is shown in the top middle panel, and the model corresponding to cos i =0.87 and [Fe] = 2 is shown in the bottom middle panel. We note that while the model with cos i =0.87 and [Fe] = 2 can better fit the region around 5 kev, it leaves some residuals between 5.5 and 6.5 kev. On the other hand the model with cos i =0.78 and [Fe] = 1.5 gives a better fit of the region between 5.5 and 6.5 kev. Because the latter seems to be better in the iron line region, this indicates that the inner radius of the disk is 70 R g, or that a more complex model is needed to fit the data. A narrow (not relativistically smeared) and not ionized reflection component is also expected from the companion star and/or the outer flared disk, and it was actually observed in ASCA and BBXRT data (Ebisawa et al. 1996, Done & Życki 1999). Adding to model 2 in Table 1 another reprocessed component, not ionized and not smeared, we obtain χ 2 /d.o.f. = 683/677, i.e. a reduction of the χ 2 by χ 2 = 6 (model 3 in Table 1). An F-test shows that this improvement is significant at 99% confidence level for one additional parameter. Also in this case we fitted

8 8 BeppoSAX data using different values of cos i and iron abundance. The resulting values of χ 2 and inner radius are reported in Table 3. In this case we obtain much smaller inner radii, around R g, sometimes as small as 6 R g, i.e. the last stable orbit in the Schwarzschild metric. The best fit has cos i =0.78 and [Fe] = 2, corresponding to R in 6 R g. With these two parameters we obtain the results shown in Table 1 (model 4). In Figure 4a we show the Cyg X 1 data fit using this model (upper panel) and the residuals (in unit of σ) with respect to the model (lower panel). The contributions to the χ 2 as a function of the energy in the iron line range are also shown in Figure 3 (lower panel). The results are subtly different from those derived from the ASCA data (Done & Życki 1999), where the best fit was for somewhat higher inclination (cos i = and [Fe] = 2), with correspondingly larger inner disk radii. We caution that at this level small uncertainties in the response and cross-calibration become important. A comparison of Tables 2 and 3 shows that the additional unsmeared component does not give a significant improvement of the fit for all combinations of inclination and iron abundance considered, so we cannot say it is unambiguously detected in our data. 5. Discussion We analyzed the broad band ( kev) spectrum of Cyg X 1 in the hard state observed by BeppoSAX. The total spectrum predicted by model 4 from Table 1 is plotted in Figure 4b. The overall spectrum consists of a complex soft component and a hard component. The former can be described by a blackbody (or disk blackbody) at kt kev and an additional component which can be described by Comptonization of soft photons in a low temperature (kt 2keV) plasma with moderate optical depth (τ 6 for a spherical geometry). This is plausible thought not a unique description the additional component can be for instance a second blackbody with kt 0.4 kev. Such a complex model for the soft excess in Cyg X 1 is in agreement with the results of Ebisawa et al. (1996) who fitted the soft component with a blackbody and a steep power-law tail. The presence of such additional comptonized excesses is not uncommon in X-ray spectra of other accreting black holes. They were previously reported in the very high and high states of Nova Muscae 1991 (Życki et al. 1998), in the high state of GRS and GRO J (Coppi 1999; Zhang et al. 2000), in the high state of Cyg X 1 (Gierliński et al. 1999) and also in the Seyfert 1 galaxy NGC 5548 (Magdziarz et al. 1998). They suggest existence of a third phase of accreting plasma, intermediate in properties between the cold, optically thick disk and the hot, optically thin matter responsible for the hard Comptonization. The origin and location of such warm plasma would be different in the three different scenarios discussed below. The hard component can be modelled as comptonized emission from a hot ( 100 kev) corona, with the corresponding reprocessed component (Fe K α line and edge, and the reflected continuum).

9 9 The reprocessed component has a small amplitude, Ω/2π , is smeared, and is not highly ionized. The best fit indicates high values of the iron abundance (2 times Solar) and moderate inclination angles (cos i = ). A second not ionized and not smeared reflection can also be present, probably from the companion star and/or an outer flared disk. Smearing of the reflected component is significantly detected in Cyg X 1. Assuming that it is due to relativistic effects, this indicates the presence of optically thick material at small radii. The value of the inner radius of the disk is strongly dependent on the inclination angle of the system and the iron abundance (and on details of the modelling and calibration). The model fits given in Table 3, using two reflected components, give values between 6 and 20 R g. Without a second reflector the inner radius can be larger ( 150 R g at most, see Tab. 2), but the fits are generally worse. These results are consistent with the inner radius of the disk inferred from the rapid timing variability properties, in the hypothesis that the QPO frequency detected in these systems is related to the innermost disk radius. In the case of Cyg X 1 in the low/hard state, R in should be less than 20 R g (depending on the mass of the black hole; Di Matteo & Psaltis, 1999). Our broad-band spectral results are in agreement with previous studies of the low/hard state of Cyg X 1 (Poutanen et al. 1997; Gierliński et al. 1997; Dove et al. 1997), where it was demonstrated that the observed spectra are incompatible with the model of an accretion disk with a static corona in a plane parallel geometry (Haardt & Maraschi 1993). In these models the soft photons emitted by the disk have to pass through the corona, resulting in a strong cooling. Therefore the predicted spectra are too soft to match the observed hard spectrum from Cyg X 1. Instead, they can be interpreted within two geometrical scenarios: a hot inner disk with cold outer disk, and a disk with active regions. We will now discuss both geometries in some detail The hot disk model In the hot disk model, the hard X-ray spectrum originates in an inner accretion flow, with electron temperature 100 kev and optical depth τ es 1. If the hot flow is heated by a viscous (αp ) mechanism (Shakura & Sunyaev 1973), the electron temperature has to be different than the ion temperature (Shapiro, Lightman & Eardley 1976), in which case T ion approaches the virial temperature, the flow becomes geometrically thick, and advective transfer of energy is important (Ichimaru 1977, Narayan & Yi 1995). Conduction of heat between the hot flow and any standard cold disk necessarily leads to evaporation of the disk if the accretion rate is smaller than a critical value (Różańska & Czerny 2000). This gives a mechanism for a transition between disk dominated and hot flow dominated accretion, though there can be a region of overlap between the two flows (Różańska & Czerny 2000), where the observed additional soft component may be generated.

10 Optical depth of the central plasma cloud We have performed Monte Carlo simulations of Comptonization in this geometry to estimate the optical depth of the central plasma cloud, and the amplitude of the reprocessed component. Approximating the complex geometry to a central, uniform density sphere and an outer cold disk, without any overlap, we find that the observed hard spectrum can be matched if kt e 90 kev and τ es 1.8. This then predicts the amplitude of the spectrum of the soft seed photons and the amount of reflected spectrum from the accretion disk. Both these predicted values are within the observed limits, if we use the comptt model to describe the soft excess. Using two blackbodies for the soft emission, the observed ratio L hard /L soft is larger than the predicted value in the above geometry, without overlap between the outer disk and the central plasma cloud. We also note that the assumed uniform sphere may not be a good approximation to a real accretion flow, where energy dissipation is concentrated towards the center The overall energetics Adopting the Comptonization model for the soft excess, we find the total flux in the hard component F hard = erg cm 2 s 1 and in the soft component (blackbody plus the soft comptonized component) F soft = erg cm 2 s 1. The bolometric luminosity of the primary source is then L tot = L hard + L soft =4πd 2 F hard + 2πd2 cos i F soft, (1) assuming isotropic emission of the hard X-ray source, and disk emission of the soft X-ray source. This gives L tot = d 2 2 erg s d 2 2 M 10 1 L Edd for cos i =0.7, where d 2 is the distance to Cyg X 1 in units of 2 kpc, M 10 is the black hole mass in units of 10M,andL Edd is the Eddington luminosity for a 10M black hole. To compute the mass accretion rate we need to take into account that a fraction of energy may be advected into the black hole. Denoting the advected fraction by f adv we obtain the total rate of viscous energy dissipation, Q + = L hard /(1 f adv )+L soft = L tot {1+(L hard /L tot )[f adv /(1 f adv )]}. The mass accretion rate is then ( Ṁ = Q + /(ηc 2 ) d L ) hard f adv gs 1, (2) L tot 1 f adv where η = is the efficiency of accretion in Schwarzschild metric. This gives ṁ Ṁ ( 0.02 d 2 2 M L hard Ṁ Edd L tot f adv 1 f adv ), (3) for Ṁ Edd = L Edd /(ηc 2 ) M 10 gs 1. For example, for f adv =0.75 (as in the solution of Zdziarski, 1998, for ṁ = ṁ crit ), ṁ 0.06 d 2 2 M 10.

11 Estimating the transition radius The transition radius does not enter the Monte Carlo simulations performed in Sec : the fraction of soft photons intercepted by the hard source is completely determined by the geometry, which is scale invariant. We can estimate the truncation radius using information from total energy budget (Section 5.1.2). This again requires the assumption that there is relatively little overlap between the two phases, and the cold disk emission is predominantly due to viscous energy dissipation rather than thermalization of the illuminating X-rays. From Eq. (1) the fraction of viscous dissipation taking place in the hot flow is Q + hot /Q+ 2/(3 f adv ). The radial distribution of energy dissipation per unit area of the disk is described by (e.g. Frank, King & Raine 1985) F (R) = 3 8π Using Eq. 4 we can estimate R tr solving Q + hot Q + = GMM 1 R 3 6R g R. (4) Rtr 6R g 2πF(R)RdR 6R g 2πF(R)RdR. (5) For a purely radiative inner flow (f adv =0)weobtainR tr 40 R g. The presence of advection increases this estimate and for e.g. f adv =0.75 we obtain R tr 130 R g. Alternatively, the inner radius of the cold disk can be estimated using the information on the blackbody soft component, assuming that this represents the emission from the inner part of a standard, optically thick, geometrically thin accretion disk. Its luminosity is then the total potential energy that has been released at R in : L BB GMṀ (6) 2R in We attribute the measured temperature of the blackbody to the maximum temperature in the disk, that is reached at the inner radius R in where the disk is truncated: ( ) 3GM 1/4 ( ) 1/4 M 6R g T max = 8πσRin 3 1 (7) R in From these two equations we can find the inner radius of the disk as a function of the measured temperature and luminosity of the blackbody. Using the values reported in Table 1 (model 4), and considering that L disk =2πd 2 F earth / cos i, wheref earth is the observed flux, we obtain R in cos i 35 R g, for a distance of 2 kpc. This should be modified as a simple blackbody spectrum does not adequately describe the emission of accretion disks in X-ray binaries, because electron scattering modifies the spectrum

12 12 (Shakura & Sunyaev 1973; White, Stella & Parmar 1988). In this case, the measured color temperature is related to the effective temperature of the inner disk T col = f col T eff,wheref col is the spectral hardening factor. The factor f col has been estimated by Shimura & Takahara (1995) to be 1.7 for a luminosity of 10% of the Eddington limit, with a little dependence on the mass of the compact object and the radial position. Applying this correction to the values of R in obtained above, we find R eff cos i = f 2 col R in cos i 100 Rg. The correction factor used here is probably an underestimate since Shimura & Takahara (1995) do not consider illuminated disks, as it is in the case of Cyg X 1. For instance the additional soft excess component could be the emission of the inner part of the disk, strongly modified by the Comptonization, which would then imply f col 4 5. However we are only considering here the part of the disk (probably at large radii) that emits the blackbody spectrum. Therefore this region is probably not dramatically influenced by the Comptonization and a factor 1.7 could be good enough for this rough estimate Summary of hot disk model The geometry with a central, uniform density, hot plasma cloud with no overlap between this and an outer disk can reproduce the overall observed emission. Energy balance and the observed soft seed photon temperature both point to a transition radius between the disk and the hot flow of 100 R g, in agreement with the estimation of the inner disk radius from the observed smearing of the iron line (assuming that this arises from relativistic effects), when only one reflection component is considered (see Tab. 2). However, this is in conflict with the smearing of the iron line in the best fit models with two reflection components. For this model to fit the observations requires either that there is further smearing of the reflected component by Comptonization (see section 5.2.2) and/or consideration of a more realistic geometry, with a hot flow which is centrally concentrated, and where there is some overlap between the hot and cold flows The active regions model Another possibility for explaining hard spectra such as those observed from Cyg X 1 and other GBHCs is a geometry of an untruncated, cold disk with clumpy active regions (Stern et al. 1995). These can be physically envisioned as magnetic flares (Galeev et al. 1979; Haardt et al. 1994). However, in order to decrease the amplitude of the reprocessed component in such a configuration, one has to postulate that either the comptonizing plasma is not static but it outflows at mildly relativistic speed, β 0.3 (Beloborodov 1999a,b), or a hot ionized skin forms on top of the disk, increasing the X-ray albedo, reducing both the amplitude of the observed reflection and the soft, thermalized flux (Ross et al. 1999; Nayakshin et al. 2000).

13 The outflow model Using the formulae from Beloborodov (1999a,b) we can estimate the outflow velocity, β (in units of the speed of light), the flare geometry (parameterized by µ s, the cosine of the angle between the midpoint of the flare and its edge as seen from the disk) and the fraction of energy dissipated in the magnetic corona, f cor, from the observed spectral index Γ 1.63, reflection amplitude f , and ratio of luminosities, L soft /L hard 0.5. Eq. (4) of Beloborodov (1999a) for the soft luminosity intercepted by the blob, can be generalized to the case of f cor < 1togive L s,blob = µs 1 [(1 a)l X (µ)+(1 f cor )L tot ]dµ, (8) where a 0.3 is the energy-integrated X-ray albedo. L tot is the total energy dissipation rate, L X = f cor L tot is the blob (hard X-ray) luminosity, and we have assumed the same distribution of emission for both soft X-ray components (the blackbody/disk-blackbody and additional soft X-ray emission). This would be roughly equivalent to assuming the covering fraction of the active regions not much less than 1, so that the spatial distribution of the disk effective temperature is roughly uniform. The angular distribution of L X in the observer frame is given by L X (µ) = L X 2γ 4 (1 βµ) 3. (9) Beloborodov (1999a) demonstrated that the soft luminosity in the comoving frame is L c s = L s,blob γ 2 [1 β(1 + µ s )/2]. The amplification factor A L X /L c s can then be directly related to the hard X-ray slope Γ 2.33(A 1) δ,whereδ 1/6 for GBHCs (Beloborodov 1999a, 1999b). Next, the observed soft X-ray luminosity, i.e. not intercepted by the blob is L soft = 0 µ s [(1 a)l X (µ)+(1 f cor )L tot ]dµ, (10) while the observed hard X-ray luminosity is L hard = L X (cos i), where i is the inclination of the system. The three observables, Γ, f and L soft /L hard, enable estimation of β, µ s and f cor (assuming the inclination is known). First, the outflow velocity can be directly obtained from the observed amplitude of reflection. For f = andcosi =0.75 we obtain β = Assuming for concreteness β =0.35, we find that f cor 0.8 andµ s 0.5 reproduce both Γ 1.6 andl soft /L hard 0.5 in the spectral model containing the comptonized excess. For the other model of the soft component (two blackbodies), which gives much smaller L soft /L hard 0.1, the coronal dissipation fraction is f cor > 0.99 while µ s 0.3. A further development of the original model by Beloborodov (1999a) may also be necessary in the light of the results on relativistic smearing of the reprocessed component. The outflow velocity has to be larger in the inner disk region than in the outer one, if the reprocessed component does

14 14 not show the extreme smearing, corresponding to inner disk radius close to the last stable orbit at 6R g. However, our results here are somewhat ambiguous and, in particular, in the model with two reprocessed components, the relativistic smearing does indeed correspond to inner radius close to R ms. The approximation with constant β(r) may thus be appropriate The hot skin model In this model, assuming the disk is radially uniform, the observed amplitude of cold reflection can be expressed as f [P trans(τ)] 2 1+P refl (τ), (11) where τ is the optical depth of the hot skin, while P trans (τ) andp refl (τ) are transmission and reflection probabilities in the hot skin (i.e. the ratio to the incident flux of the flux transmitted down through the hot skin to the cold material, and the flux reflected out of the top of the hot skin, respectively). Obviously, for a pure scattering layer P trans (τ)+p refl (τ) = 1. We obtained both probabilities from Monte Carlo simulations in a slab geometry. The observed amplitude, f rel 0.3 corresponds to P trans (τ) 0.64 and τ 0.7. The ratio of the soft thermalized flux to the primary hard X-ray flux is (1 a)p trans (τ)/(1 + P refl (τ)) 0.4, close to that observed in the model with the additional soft excess component described as comptonized emission (see Section 5.1.2). Indeed one could imagine that this additional component is the disk emission comptonized in the hot skin, as the photons diffuse through it. The expected ratio of fluxes of the blackbody component, F bb, to the comptonized soft excess component, F sxe,isf bb /F sxe P trans /[A(1 P trans )], where A is the Compton amplification. For an optical depth of 0.7, F bb /F sxe should thus be 2(A 1 1 here), while from the best fit model we infer F bb /F sxe 4. Also, for an optical depth of 0.7 the spectral shape of the additional comptonized component requires that the temperature of the hot skin is kt skin 12 kev. This is a little high compared to the mean Compton temperature in the skin of kt IC 5 kev (Nayakshin et al. 2000). The diffusion of the reprocessed photons through the hot skin results in smearing of iron spectral features due to Comptonization. We have modelled this by convolving the reprocessed spectrum with the Comptonization Green s functions of Titarchuk (1994). The smearing in the data is consistent with Comptonization alone for kt skin =12keVandτ =0.7: fitting only MECS data in the 4 10 kev band we have found that Comptonization smearing gives χ 2 /d.o.f. = 130/126 while relativistic smearing gives χ 2 /d.o.f. = 127/125. However, in the hot skin model, there is no reason for the disk to be truncated, and so both smearing mechanisms would operate. The relativistic smearing would be that expected from a disk extending to 6 R g, although with emissivity going to zero at the last stable orbit (Shakura & Sunyaev 1973), F irr (r) r 3 (1 6R g /r). We have found that the model with both the relativistic smearing (with the inner radius fixed at 6R g ) and Comptonization smearing (with fixed τ =0.7 andkt = 11 kev) gives a rather bad fit,

15 15 χ 2 /d.o.f. = 150/126. The problem may be avoided by postulating that the hot skin is thicker closer to the black hole (Nayakshin 2000), thus reducing the reflection amplitude from the inner regions Summary of untruncated disk models A fundamental problem is the high coronal dissipation required for these magnetic flare models. The maximum which has so far been produced in current (though admittedly incomplete) simulations is f cor 0.25 (Miller & Stone 2000), while the data imply f cor > 0.5. Apart from this the plasma outflow model can reproduce the observations, though the complex soft excess is unexplained. The hot skin model gives qualitative origin for the soft excess as Compton scattering of the disk photons, but quantitatively this does not give what is observed. Also the Comptonization in the hot skin gives an additional smearing of the iron line and the reprocessed spectrum, and this smearing is much larger than that observed. However, if the model is extended to allow radial stratification of the depth of the hot skin then this may allow both the soft excess and line smearing to match that observed. 6. Conclusions Broad band kev BeppoSAX data from Cyg X 1 in low/hard state can be described by a complex soft component and a comptonized hard component with the corresponding X-ray reprocessed spectrum. The soft component can be decomposed into a low temperature (kt 0.1 kev) blackbody emission, presumably from the accretion disk, and an additional component which can be modelled as Comptonization of the disk emission by a low temperature (kt 2keV)plasma. The hard comptonized component corresponds to a spectrum with photon index 1.6 with a cutoff at the electron temperature of the corona, kt e 100 kev. The reflection spectrum consists of a weakly ionized, smeared component. Assuming that this broadening is due to relativistic smearing, this corresponds to an inner disk radius of 70 R g or 10 R g (depending on the inclination of the system). A non-smeared component, due to reflection from the companion star and/or a flared outer disc, might also be present. In this case we find that the inner radius of the disk, as deduced by the reflection component, is smaller, 6 10 R g. The spectrum is broadly compatible with the three major scenarios proposed for emission in GBHCs, although all need some modification to fit the data. These are: (1) a hot (kt e 100 kev), optically thin(ish), inner flow and a cold outer accretion disk, an accretion disk with active regions with either (2) mildly relativistic outflow (v 0.3c) of the comptonizing plasma or (3) a hot (kt 10 kev), ionized skin. We thank B. Czerny and A. Zdziarski for useful discussions. This work was supported by the Italian Space Agency (ASI), by the Ministero della Ricerca Scientifica e Tecnologica (MURST) and

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19 19 TABLES Table 1: Results of the fit in the energy band kev. Error bars correspond to χ 2 =2.7. Blackbody flux is in units of L 39 /D 2 10,whereL 39 is the luminosity in units of ergs/s and D 10 is the distance in units of 10 kpc. thcomp normalization is in photon cm 2 s 1 at 1 kev. f =Ω/2π is the reflection amplitude (f = 1 corresponds to the amplitude of reflection expected from a slab subtending a 2π solid angle around an isotropic source) and ξ is the ionization parameter, ξ = L X /n e r 2. Parameter Model 1 Model 2 Model 3 Model 4 N H ( cm 2 ) ± ± kt BB (kev) ± ± ± F BB kt comptt (kev) τ comptt N comptt Photon Index ± ± ± ± kt e (kev) 111 ± N thcomp ± ± f rel ± ± Fe abund 1.0 (fixed) 1.0 (fixed) 1.0 (fixed) 2.0 (fixed) cos i 0.6 (fixed) 0.6 (fixed) 0.6 (fixed) 0.78 (fixed) ξ R in /R g f narrow ± ± 0.03 χ 2 /d.o.f. 713/ / / /677